Question

If \( x \) is inversely proportional to \( y \) and \( x = 10 \) when \( y = 2 \), what is \( x \) when \( y = 8 \)? Options

• A. 1.5
• B. 2
• C. 2.5
• D. 4

Hint:

In inverse variation, the product of the two variables remains constant: \( x \times y = k \).

Answer 1

The Correct Option is C

We are given that \( x \) is inversely proportional to \( y \). This means that the relationship between \( x \) and \( y \) can be expressed as: \[ x = \frac{k}{y}, \] where \( k \) is a constant of proportionality. Step 1: Find the constant \( k \).
[6pt] We are given that \( x = 10 \) when \( y = 2 \). Substituting these values into the equation to find \( k \): \[ k = x \times y = 10 \times 2 = 20. \] Step 2: Use the constant \( k \) to find \( x \) when \( y = 8 \).
[6pt] Now that we know \( k = 20 \), we can find \( x \) when \( y = 8 \). Substituting \( k = 20 \) and \( y = 8 \) into the equation: \[ x = \frac{k}{y} = \frac{20}{8} = 2.5. \] Conclusion:
[6pt] The value of \( x \) when \( y = 8 \) is: \[ \boxed{2.5}. \]